GATE ME 2017 Set 1 — Question 63
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Let be the plane figure consisting of the points given by the inequalities and . Let be the plane figure given by the inequalities , , and . Let be the union of and . The area of is
Correct answer
(C) 32
Solution
1.Analyze :
..
is a rectangle with width and height .
Area() .
2.Analyze :
, , .The vertices of this triangular region are:
- Intersection of and :
- Intersection of and : . Point:
- Intersection of and : . Point:
Area() .
3.Find Area of :
covers the region and covers the region for the same -range .The intersection is the line segment for , which has zero area.
Area() = Area() + Area() = .
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